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The collision happen after the car in front stopped
\begin{eqnarray}
\frac{v_1^2 - v_0 ^ 2}{2a_0} + v_1 t_r - l & = & \frac{v_2 ^ 2 - v_0 ^ 2}{2a_1}\\
\frac{v_2 - v_0}{a_1} & = & t\\
\frac{v_1 - v_0}{a_0} & = & t - t_r
\end{eqnarray}
The collision happen before the car in front stopped
\begin{eqnarray}
v_2 t_r + \frac{v_2 ^ 2}{2a_2} - l& = &\frac{v_1^2}{2a_1}
\end{eqnarray}
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